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Jack walked up a hill at a speed of x^2 - 11x - 22 miles per hour. Meanwhile, Jill walked a total distance of x^2 - 3x - 54 miles in x - 9 hours. If Jack and Jill walked at the same speed, what is that speed, in miles per hour?

 Dec 30, 2020
 #1
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Jill's speed  =   distance  / time

 

So    equating speeds

 

x^2  - 11x   -22   =   (x^2    - 3x  - 54)  / ( x - 9)

 

x^2  - 11x  - 22  =  ( x - 9) ( x + 6)  /  (x -9)

 

x^2  -11x  - 22  =  x +  6       subtract the right side ftom  the left and we  get that

 

x^2  - 12x - 28   = 0       factor as

 

(x - 14) ( x + 2)  =  0

 

Setting  both factors to 0  and solving  for x produces

 

x  =14       or  x   =   -2

 

When x   = 14    the speed   is    (14)^2 -11(14)  - 22  =  196 - 154 - 22  =    20 mph   (pretty fast)

 

When x  =  -2    the speed is   (-2)^2  - 11(-2)   - 22  =   4 + 22   -22   = 4 mph   ( this answer  is reasonable)

 

 

cool cool cool

 Dec 30, 2020

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